Engine just clicks when cranked. battery is brand new. where is the starter??

Regardless of the battery being new, #1 priority is to make sure the battery is fully charged.

Did you test the battery or starter before replacing them or just buy new thinking that would fix your issue?

Is it cranking at all? Do you hear a click when you try to start the car? Are the lights on the instrument panel working, do the headlights work?
What make/model/year vehicle is it? Are you getting a security light warning on the instrument panel, if yes, do you have a different ignition key that you usually use.

These answers would help identify a problem.

If it's not a security issue, turn the headlights on and then try to start the car. If the headlights dim it indicates a problem with the starting system. If the lights go completely out it usually indicates bad electrical connections. If the lights go out completely clean your terminal connections, check your ground connection to the vehicle/engine and try again.

This is the time period when GM had ign switch problems. Get a voltmeter and wiring diagram and check the IGN switch

Could be the starter relay but , could also be the park neutral safety switch , test by moving the gear selector to neutral . If it starts then more then likely the PNP switch is bad . Viewing wiring diagrams to see what all is involved in starter operation . Reading factory service info. for starter operation would be good too . The engine computer (PCM/ECM) probably energizes the starter relay . Free wiring diagrams here http://www.bbbind.com/free-tsb Enter vehicle info. year , make , model an engine . Under system click on engine , then under subsystem click on starting . Click the search button , then the blue link . Looking at the wiring diagram it just so happens there is no starter relay . Ignition switch sends battery voltage through the PNP directly to the starter solenoid . Could be the main battery cable , voltage drop testing will show if that is the problem .
Starter Voltage Drop

is the engine siezed ?? try another battery from a known car that starts ,a battery can show 12.4 or more on the meter but have no reserve amp capacity to make it it crank ,this i get on modern batteries owing to the fact their sealed unit so you cannot check the water level in them ,,,,use a hammer and chisel and break the sealed for life top off and you will see what i mean

hook a volt meter up to your battery you should see around 12.5 volts. Then crank the engine and see what the voltage drops to. If it drops to less than 12 volts the battery is bad.

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try and turn engine by hand to make it is not seized .if ok it may have a bad electoral connection either from battery to starter or from battery to engine earth, voltage drop can be checked with a volt meter.

Park neutral safety switch maybe be the reason for the no crank ! Try putting the vehicle in park ,then try to crank the engine . Testing the electrical circuit is the best way to trouble shoot this problem , along with do a voltage drop test on the starter circuit ! This will test the battery cables an connections .
Starter Voltage Drop
How to voltage drop test starter motor circuit
Does it have a manual or automatic transmission ? Manual ? clutch switch . Looking at a wiring diagram I also see a starter cut relay !
http://www.bbbind.com/free_tsb.html Free wiring diagrams . Enter vehicle info. year , make , model and engine size . Under system click engine , under subsystem click starting . Then click the search button , then click the blue link ! Check the starter cut relay also . Videos on youtube showing how to test a relay controlled circuit !

More than likely the charging system is not working and allowing the battery to run down/low. Put a voltmeter on the battery and raise the engine about 2000 rpm and the battery should read 13.5-15.5 volts with all electronics on (fans switch on high, flashers, wipers, headllights, defrost etc). It should also read about 13.5 volts at idle but may not depending on the load from the accessories and voltage regulator. Most important is that it will read 13.5-15.5 volts when the engine is at 2000 rpm with the accessories on. If it does not read in that range the charging system(alternator most likely) has a charging problem.

Check the igntion signal to the starter solenoid.

That would be your starter solenoid clicking, the positive battery cable runs off the battery to it, easy way to track it down, you can test it by putting your ignition key in the on position and using a jumper wire connect the two large terminals, if the car starts replace the starter solenoid, if it doesn't do anything replace the starter.