追 has the meaning of "to follow" as in "follow a T.V. drama" ( loyally watch every episode of the series as they come out)
To follow a TV. series is 追看 (follow and watch) E.g. 很多人都在追'中国好声音' (Many people are following 'The Voice of China')
To follow a serialized novel is 追閲 (follow and read) E.g. 少時候我有追古龍的小說 (When I was young, I followed the novels written by Gu Long)
由嘎唱的剧，必须追一下. -- you must follow (and watch) the drama series that has its theme song sung by Ga
由嘎唱的剧 -- (the drama series sung by Ga) -- Obviously, he can't sing the drama series, we can presume the comment meant he sung the theme song
[V] + 一下 = "try to [V]" or "[V] for once"