Do I put a moisturizer on over the tretinoin cream?

Tretinoin is a topical (applied to the skin) form of vitamin A that helps the skin renew itself.
The Retin-A and Avita brands of tretinoin are used to treat acne. The Renova brand of tretinoin is used to reduce the appearance of fine wrinkles and mottled skin discoloration, and to make rough facial skin feel smoother.

Tretinoin can cause skin dryness and irritation and the use of a moisturizer prevents excessive dryness.
Tretinoin is usually applied to the skin once a day at bedtime to clean, dry skin. Do not use a moisturizer immediately after applying tretinoin.
In the morning wash your face with a mild facial scrub or rough wash cloth. This will help reduce the noticeable flaking.
After washing, apply a good water-based moisturizer. Try using a moisturizer that also contains a sunscreen. If not, apply sunscreen anytime you are in the sun even for a short amount of time. Tretinoin makes you more susceptible to sunburn. You can apply extra moisturizer throughout the day as needed.

For more information see https://www.drugs.com/mtm/tretinoin-topical.html