Since she had given up smoking, she has been looking good.
or
Since she gave up smoking, she has been looking good.
Shouldn't it be "had given up"?
Since she had given up smoking, she has been looking good.
or
Since she gave up smoking, she has been looking good.
Shouldn't it be "had given up"?
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.
You can't use HAD GIVEN UP as the action described in this part of the sentence doesn't happen BEFORE ANOTHER past action. Compare: She had given up smoking before she was 25. It means she did something (gave up smoking) before some other event in the past (she was 25). One is earlier than the other. Moreover, if "since" means " from the time when", we always use past simple after it.
You do not make it clear whether since is being used in the sense of as, or from the time when.
In either case the first sentence is NOT IDIOMATIC. But the second does work with from the time when, but does not work with as.
Recommended changes.
As she had given up smoking, she had been looking good.
From the time when she had given up smoking, she looked good.
As she gave up smoking, her finances improved.