Q.Mexican Fan Palm In Pot
Pot is not very large (about 3ft. high and 2 feet across). Palm tree is about 3 feet high (from bottom of stem to highest fan peddle) and still getting new growth (recently). My question is how long can it stay in this size pot and continue to grow before it needs to be planted in the ground or put in larger pot? When is it needed to be transferred to continue growing, how I you tell when it is time?

Certified GKH Gardening Expert
You will not have to transplant until you see roots on top of the soil, or coming out of the drainage holes.
Here is an article to help you care for the Palm:
https://www.gardeningknowhow.com/houseplants/fan-palm/growing-mediterranean-fan-palms.htm