You need to relog after we you purchased booster packs , After relogging press F4 and go to the donations tab and you can claim your booster packs there.
Just check it did actually go through, Click on ZARP VIP on the forums and then check how much boosterpacks you've got then rejoin the server and press f4 then head to Donate and then click Activate Boosterpacks.
Its possible that the purchase didn't go through. Check your transaction history, if it went through or not. If it did go through it should be available for you in game. Otherwise try emailing one the owners zarpgaming.com/index.php/help/contact