I am about to sell a beach condo (I have never rented it) and will have a capital gain. If I buy another 2nd home of greater value, can I defer the capital gains taxes? I may later sell my primary residence and move into the 2nd home as a retirement home.

Are you taking about the US taxes? In the US, there is no concept of deferring the gain.

You can exclude gain of up to $250,000 on your main home or second home.
Read: Your U.S. Tax Return: Profit From the Sale of Your Home