When partner overcalls a minor and you have support (or tolerance—two or more cards) but you also have a decent 5-card major, you should MENTION your major rather than simply raising partner. Majors are cheaper games and partner can retreat to the minor if needed. So, 1♦ on your left; 2♣ by partner; 2♥ on your right and you have ♠KJ10xx ♥Qxx ♦x ♣Qxxx Go ahead and bid 2♠ rather than 3♣. Partner can retreat to clubs if she hates spades—knowing that you EITHER have club tolerance OR a good enough suit to rebid over 3♣. (You don't voluntarily come in on a misfit auction so you promise EITHER club support/tolerance OR a long, rebiddable suit of your own.)
The reverse does NOT hold. If partner overcalls a major, and you bid a minor, you are RUNNING as quickly as possible and often have NO tolerance—unless as mentioned in earlier post—your bid is at 4 level or higher. So, 1♥ on your left; 1♠ by partner; P; 2♣/2♦ by you—you have a 5 card or longer decent suit and a scattering of values. You may loath and detest spades—often a singleton or a void—and you are attempting to improve the contract. Partner should not rebid spades unless s/he has a GOOD six or more. A typical hand for you would be ♠x ♥Kxx ♦KJ10xx ♣QJx.
If your hand is weaker, do NOT bid immediately. Since the bid is at the one level, LHO will almost certainly either bid again or make a reopening double. If LHO makes a reopening double and (worst case) RHO passes (converting to penalties), THEN you trot out your long suit and hope. For example, with ♠— ♥xxxx ♦KJ10xxx ♣Qxx, you wait for reopening double by LHO and pass by RHO, then you try 2♦ and hope.
Be careful not to confuse these situations with those when you have SHOWN support already. A new suit when you have already shown support is indicating WHERE YOUR VALUES ARE so partner can make a more informed decision about how high to compete. So, for example, 1♠ by partner, 2♣ by RHO; 2♠ by you; 3♣ by LHO; pass by partner; pass; if you now bid 3♦ or 3♥, you are showing a maximum raise to partner and values in the red suit which you bid. Then, partner can decide whether to bid only 3♠; go to game if you have uncovered a double fit; or double 4♣ if they opponents try that. Example hand might be: ♠xxxx ♥AKJ10 ♦Qx ♣xxx OR ♠xxxx ♥Qxx ♦KQJ10 ♣xx. Such bids also indicate safe suits for partner to lead if your side ends up defending.