I have recently installed a new ROM on my Galaxy S3 and I did not flash gapps with the ROM itself. Can I go to reboot mode and flash gapps even after I installed the ROM?
You should be able to do that. First make sure you download the correct version (the version of the GApps archive must match the Android version installed on your device). Put the
gapps*.zip file on your SDCard, and boot to recovery-mode. Select "Install update.zip", and navigate to your GApps archive. Select it, have it installed, reboot, enjoy :)
Flash it using recovery, but you will need to wipe your cache's after flashing or gapps will crash, therefore making your phone unusable and forcing you to wipe.