May one buy and wear a new Tallis during Sefira?^[1]  

It is permitted to buy and wear a Tallis Katan during Sefira, as explained above. It is likewise permitted to buy a Tallis Gadol during Sefira, as explained above. However, due to the above-mentioned stringency regarding wearing, one should wait to wear the Tallis Gadol until Shabbos. If, however, one’s current Tallis Gadol is Pasul, and he does not have another one available, and is unable to borrow one in its place, he may purchase and wear a new Tallis Katan/Gadol.^[2]

[1] Igros Moshe 3:80 regaridng three weeks

[2] So rule regarding three weeks: Sheilas Yaavetz 82; Pischei Olam 23; Kaf Hachaim 551:92