In order to only publish an ad to an existing ad set all you need to do is the following:
1. Ensure the ad/creative you wish to publish is visible in the 'Create ads' tab:
2. Navigate to the 'My campaigns' tab, select the relevant campaign/ad set and click 'Add creatives':
3. Set Tracking settings if desired and click on 'Add x creative(s) to 1 ad set':
Please note that the objective of the new creatives needs to match the objective of the existing campaigns/ad set.