Hi @jenny chan ,
first of all: If you deleted the Authenticator app without any backup there is no option to recover the MFA codes.
You didn't mention/name the "another application". To reset/recover the MFA code/option you have to follow the "other application" vendor's process to reset/recover the MFA code.
The Microsoft Authenticator app works as a "number generator" only and the management of the MFA is handled/processed by the vendor of the "other application".
(If the reply was helpful please don't forget to upvote and/or accept as answer, thank you)
Regards
Andreas Baumgarten