With 13 HCP you should open the bidding. If you have 5 cards in a major suit you want to open 1 of that major.
Therefore to open the bidding 1♠ you need 13 HCP and 5♠. That's it.
When partner opens 1♠ we no longer need 13 points to make a bid. Since partner opened the bidding they have the opening hand. We just need 6 HCP to respond. With 6 HCP we need to respond. To support partner's ♠ suit we should have 3 cards in the suit. (Partner needs 5 cards in the suit to open remember. So to get an 8 card fit we only need 3.)
If partner opens 1♠ and you have a fit you should probably tell partner about it right away.
The only bids that limit your hand are 1NT and 2♠. Both these bids limit your hand to 6 to 10 points and partner can pass both those bids.
If you respond with a new suit at the 2 level you must have at least 10 HCP. Therefore sometimes you might have a hand with a long suit that you can't tell partner about because you don't have enough points. You might get stuck bidding 1NT with an unbalanced hand. Such is life.
Therefore if your partner opens the bidding 1♠ here is a table that states your only possible responses if you have 6 to 9 points:
Bid
Points
Number in suit
1NT
6 to 10 points and
No 3 card ♠ suit
2♠
6 to 10 points and
at least 3 ♠
This is actually easy since there are not very many choices as to what to say when partner opens 1♠ and you have between 6 and 9 HCP. You either bid 2♠ with a 3 card ♠ suit or 1NT if you have fewer than 3♠. Pretty easy when you think about it.
With that in mind what do you respond when your partner opens 1♠?
Hand 1
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