Wiktionary
cosying up
vb. (present participle of cosy up English)
Usage examples of "cosying up".
Hudson Hurst was cosying up to each Cabinet member in turn to ask for support.
It was a safe location because Estonia was cosying up to the West, yet Russians could still travel there freely without a visa or passport.
They should all stop cosying up to him - and kick him back where he belongs!