"Since she had given up smoking, ..." or "Since she gave up smoking, ..."?

Solution 1:

There is a relationship you have to keep between the tenses in the two clauses of since, when it means from the time when. If you don't have this relationship, we interpret since to mean because. See this website.

The relevant quote from this site:

When since introduces an action or event at a point of time in the past, we can use the past simple or present perfect after since and the present perfect in the main clause.

In this case, I think because I'm American, I greatly prefer the simple past in the first clause.

What this means is that the possible combinations of tenses are:

Since she gave up smoking, she has been looking good.
Since she has given up smoking, she has been looking good.
Since she had given up smoking, she had been looking good.

While the linked site doesn't mention the third possibility, it's grammatical and can be obtained from the either of the first two sentences by backshifting.

The since in both of these could also mean because, although it probably wouldn't be interpreted that way. If you want it to mean from the time when unambiguously, you have to use ever since.