Kesset HaSofer (a compendium of the laws of scribal writing by the author of Kitzur Shulchan Arukh) 25:5 (here, quoted here) writes it is forbidden to turn a strap around and re-tie it so that the end that beforehand was below is now above near the kesher, because it lessens the kedusha of the end that beforehand was above.
If the strap of the shel yad was broken near to the knot, it is forbidden to take the strap out, turn it round, and use the other [less worn out – Maḥatzit ha-Shekel.] end to make the knot, and knotting in the broken end, which used to have the knot in it, below. This is because doing so reduces its sanctity; it used to have the yud in it, and now it is being used for the wrapping (Magen Avraham, and see the Maḥatzit ha-Shekel) – and if the strap was shorter now, he just shouldn’t wrap it so many times around his arm. Even if he discarded the broken part, assuming he had enough left over, he shouldn’t turn it round, but he should make the knot as close to its original location as possible (Peri Megadim).
Therefore, if the strap is long enough, the Kesset HaSofer would permit cutting the broken part, putting it in geniza and retying the knot with the upper part of the (now shortened) strap.
PS. Cutting the strap is not an issue, many sofrim will do this as straps tend to be sold in formats which are too large for most men (I discussed it no later than two days ago with a sofer). This is also the ruling of dinonline. But one has to be careful to put the discarded piece of strap in geniza (SA OC 154:3). See also this related question: Cutting Tefillin Retzuos
As always here, CYLOR and don't trust strangers on the Internet.