Please eat if you’d like.
You've seen that 召す can mean "to respectfully eat," so adding 上がる, "to rise," means you're lifting the other person up. In polite language you use this when you're talking to someone higher up than you so you have to raise the humbly eating up. So it still means to respectfully eat, but raising it makes it a higher politeness level.
This is a combination of the words 召す and 上がる that you learned already. 召す becomes 召し and then you add that to 上がる. Pretty straightforward, right?