Are you permitted to tie new tzitzis on an old beged during the Nine Days? Would it make a difference if your current tzitzis weren't passul, but just looked ratty?
Additionally, what about buying a new tallis katan altogether?
I'm inferring from Ram"a on O.C. 551:3 that buying a new tallit kattan would be permitted during the 9 days as this is for the purpose of a mitzvah. (See Ram"a about 8 lines down, who says ... אם לא לצורך מצוה.)
I would further infer that tying tzizit on an old begged should be less of a concern. Not only is this לצורך מצוה, but if you were tying it onto a non-freshly laundered garment, I really couldn't see a problem. However, because of לצורך מצוה, I think it would be fine even if you tied it onto a just laundered garment.