I am currently writing an essay about our national hero but I am not sure whether to use 'had' or 'have' in this sentence:
He may have died early, but he sure have/had contributed a lot for our country.
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If you use has (note that have is used for I, you, we, they), implies there's a result in the present. If you use had, implies that an event passed before another event in the past.
After he died, the contribution he made happened before.
Now may have died is for possibility in the past, perhaps dead or not, he made the contribution before.
He may have died early, but he sure ? contributed a lot for our country.
A verb must always match the number (singular/plural) of the subject. That already rules out "have".
A verb must also match the desired tense (present/past/future/...). Your first part of the sentence concerns a person who has already died (present state due to past event; present perfect). The contributions of that person can only be made prior to that past event of death, so they are past contributions. The question is whether you want to convey that those contributions have resulted in a present state ("has contributed") or that they had resulted in a past state ("had contributed").
Neither is really suitable. "Have" is not singular, and "had" sets the contributions too far back in the past, behind some other past event.
"Has" is possible, if you wish to emphasize that, up to the present day, the contributions have continued to be significant (and imply that they have in fact continued to be made).
But the most natural construction here is to simply leave out that word altogether, using the simple past tense. "He sure contributed a lot for our country." This puts the contributions into the more immediate past (going as far back as needed, but no further).
If you want to shift the emphasis a little more, perhaps to allow for better stress in a speech, you could adjust it to use a different auxiliary verb: "He sure did contribute a lot for our country." Again, this is simple past tense. ("Contribute", like all verbs, becomes a bare infinitive after any form of "do".)
As Nathan said,
He may have died early, but he sure has contributed a lot for our country.
would be the right way.