In the following sentence, should I use "have" or "has?"
Your generous support, trust and commitment has sustained us over the years and is more important than ever in the coming year.
Generous support, trust and commitment are multiple items (plural) and as you or I aren't included in the list so it's third person. Have is only altered to "has" in single third person (he, she or it), so it stays in "have". Hope it helps!
Your generous support, trust and commitment have sustained us over the years and will be more important than ever in the coming year. There is a compound subject, so you need a plural verb. I also suggest the tense-sequence works better as corrected
I find it useful to simplify the sentence while keeping the same structure, like so:
Your horse, dog, and cat have entertained us throughout the years.
Whereas the other variant does not sound right:
Your horse, dog, and cat
hasentertained us throughout the years.