Will putting my ETH into a wallet continue to make me a profit if the price rises?

I put a chunk of money into ETH when it crashed and it’s made me a little bit of profit so far. If I move all my ETH to a wallet does it continue to go up/down with the market? Or will the amount stay the same until I decide to sell it?

At the moment i’ve just got all my crypto in an exchange, but I’m worried about safety/longevity as my portfolio grows.