"Getting better" is generally expressed with the word "feabhas" ("excellence, improvement").
Ba mhaith liom feabhas a chur ar mo chuid Gaeilge = I'd like to improve my Irish
Chuaigh mo chuid Gaeilge i bhfeabhas/Tá feabhas ar mo chuid Gaeilge = My Irish has improved
You can also use "fearr" ("better") in some cases:
Léim Gaeilge níos fearr anois = I read Irish better now
Ba mhaith liom Gaeilge níos fearr a labhairt = I want to speak better Irish
When talking about "getting better" in the sense of "recovering from an illness", "biseach" is better:
Bhí mé tinn ach tá biseach orm anois = I was sick but I'm better now