gain ground on
• get closer to someone or something that is ahead in a pursuit or competitive situation.
• "the dollar gained ground on all other major currencies"
gain ground
• become more popular or accepted.
• "new moral attitudes are gaining ground"
Similar:
make headway,
make progress,
make strides,
progress,
advance,
proceed,
move,
get on,
get ahead,
come on,
come along,
be getting there,