strike up a friendship

strike up (something)

To initiate, instigate, or begin something. I saw you striking up a conversation with Jack—what did you two discuss? You might be able to strike up a deal with her if you mention your father's connection to the business. The detective and the con man struck up a unique friendship.
See also: strike, up

strike up a friendship

to become friends (with someone). I struck up a friendship with John while we were on a business trip together. If you're lonely, you should go out and try to strike up a friendship with someone you like.
See also: friendship, strike, up