May one order clothing during the three weeks and nine days if it will only arrive after Tisha B’av?

Yes.[1]  However, some Poskim[2] rule one may not do so during the nine days.

[1] Igros Moshe 3:82; Vayivarech David 69; See Piskeiy Teshuvos 551:11 footnote 75

The reason: See Rama 551:7 that one may have a non-Jew make one clothing for it to be ready after the fast; Thus, from here we see that so long as the garment will not be received by the buyer until after the fast, it is permitted. This is in contrast to laundering, which is forbidden even for after the fast. See M”A 551:25 that buying is more lenient than laundering, and so long as “his name is not yet on the clothing”, it is permitted; Another aspect we can add, is that no Kinyan Meshicha has been made until one receives the product and hence it is not yet his; See Vayivarech David 69; Piskeiy Teshuvos 551:11 footnote 75

[2] Piskeiy Teshuvos 551:11 footnote 75