Jan,
You may be able to take up the little movement you need by moving the slip joint a little at the ZF end....much easier.
That turnbuckle looks pretty solid, but if you do need to undo it first use a pen or marker to mark alignment of the two rods with each other. Then hold #2 whilst undoing jam nut #3 and then undo jam nut #1 (should be left hand thread). Once all is loose you can move the turnbuckle clockwise (as looking at your photo) to extend the rod length. It likely won't take much as the threads are fairly coarse. The trick is then to hold it all there while retightening the jam nuts and ensuring the marks on the rods are aligned. If you don't do that part then you might change the cross gate (R-5) centering as well.
Good luck,
Julian
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