Do you mean in a situation where you own the shares and already sold a covered call on them? In that case, I would let the shares get called away (instead of taking a loss on the call and selling a new one at a higher strike). That’s just me though. If you really want to hang onto the shares, then you could roll it up to a higher strike and out to a later expiration date.

If you own the shares but haven’t sold a call on them yet, it depends. Are you wanting to sell the shares immediately because you’re worried the price could drop in the near term? If so, sell the shares and start over with the cash secured puts.

I, personally, would sell a covered call because it’s like setting a limit sell order. If the shares get called away, great. You were able to keep some premium and make a little gain from the sale of the shares. If it doesn’t get called away, I can just continue selling covered calls and collecting premium. This is assuming it’s a stock I like, I want to keep, and am okay with possible unrealized losses on them in the short term.