This shop has been around for a while, but it became famous after it was shown on TV
This shop has been around for a while, but
このお店は前からあったけど
been around for a whileは前から(例えば3年以上）あったお店などについて使う表現です。
it became famous after it was shown on TV
テレビで紹介されて有名になった
直訳的なwas introduced on TVでも通じますが英語でwas shown on TV (見せられた)やappeared on TV（出た、現れた）という表現の方が多く使われています。
ご参考になれば幸いです！
This store has been here for a while but it got famous after being put on television.
"このお店は前からあったけどテレビで紹介されて有名になった"
- This store has been here for a while but it got famous after being put on television.
- This place has been around for quite some time but after being featured on television, it got really famous.
「このお店は昔からずっとあったんだけど、外国のテレビで紹介されて一気に観光スポットになった」
- This place has been around for quite some time but it got featured on television overseas and instantly became a tourist attraction.
アメリカ合衆国 
