Two possible versions of "everything" are .+ and .*. The . means "any character", the + means "one or more" and the * means "zero or more". So, .+ means "one or more of any character" and .* means "zero or more of any character".
One way to say "after an _" is to say "look back for an _". The is done with "(?<=_)". You can say "look back for an _ and match one or more of any characters until the end of the input" with (?<=_).+$. The $ means "the end of the input".
str_extract(c("ert_67fgt","cvcfd_kio"),"(?<=_).+$")
[1] "67fgt" "kio"
Another way to match from an _ to the end of the input is to say "match one or more of any character that is not an _ until the end of the input". The expression for "not an _" is [^_], so the full expression is "[^_]+$"
> str_extract(c("ert_67fgt","cvcfd_kio"),"[^_]+$")
[1] "67fgt" "kio"