The Collaborative International Dictionary
On the make
Make \Make\, n. Structure, texture, constitution of parts; construction; shape; form. It our perfection of so frail a make As every plot can undermine and shake? --Dryden. On the make,
bent upon making great profits; greedy of gain. [Low, U. S.]
seeking higher social status or a higher employment position.
seeking a sexual partner; looking for sexual adventure.
Wiktionary
on the make
a. 1 (context idiomatic English) Actively seeking a romantic encounter or relationship. 2 (context idiomatic by extension English) Actively seeking an opportunity for self-advancement; eager to ingratiate oneself to others in order to secure some advantage.