Turn out, develop; see take shape.
Improve so as to meet a standard, as in The coach told the team that they'd better shape up or they'd be at the bottom of the league. This usage was first recorded in 1938.
shape up or ship out Behave yourself or be forced to leave, as in The new supervisor told Tom he'd have to shape up or ship out. This expression originated in the 1940s, during World War II, as a threat that if one didn't behave in an appropriate military manner one would be sent overseas to a combat zone. After the war it was transferred to other situations calling for improved performance.