user17228: Situation: there's a piece between the king and an opponent’s piece. If this piece were not there, it would be a check.
If I were to try and move the protecting piece somewhere and leave the king exposed, that move would be not allowed.
Could I move this protecting piece, even though when it's lifted the king is in check, but when the piece lands, the king is protected again?

user7657: Yes, you can move as you've described since you haven't broken the pin, which remains in effect.  You just can't move the piece so that the king becomes exposed, which would be an illegal move.  

user12629: Yes, that's legal.  For example:
[FEN "6k1/6r1/8/8/8/6R1/8/6K1 w - - 0 1"]
[SetUp "1"]
[CurrentPosition "6k1/6r1/8/8/8/8/6R1/6K1 b - - 1 1"]

1.Rg2

The rook can move along the g-file.  This is known as a "partial pin" - the rook is somewhat limited in its movement (and can't go to a3, for example) but it can still move if it still protects the king.

17228: <p>Situation: there's a piece between the king and an opponent’s piece. If this piece were not there, it would be a check.</p>

<p>If I were to try and move the protecting piece somewhere and leave the king exposed, that move would be not allowed.</p>

<p>Could I move this protecting piece, even though when it's lifted the king is in check, but when the piece lands, the king is protected again?</p>
 7657: <p>Yes, you can move as you've described since you haven't broken the pin, which remains in effect.  You just can't move the piece so that the king becomes exposed, which would be an illegal move.  </p>
 12629: <p>Yes, that's legal.  For example:</p>

<pre><code>[FEN "6k1/6r1/8/8/8/6R1/8/6K1 w - - 0 1"]
[SetUp "1"]
[CurrentPosition "6k1/6r1/8/8/8/8/6R1/6K1 b - - 1 1"]

1.Rg2
</code></pre>

<p>The rook can move along the g-file.  This is known as a "partial pin" - the rook is somewhat limited in its movement (and can't go to a3, for example) but it can still move if it still protects the king.</p>
