Grow old or older:
— Young men senesce.

synonyms: age, get on, maturate, mature.

Roget 124: be old etc. adj.; have had its day, have seen its day; become old etc. adj.; age, fade, senesce.   

Roget 128: be aged etc. adj.; grow old, get old etc. adj.; age; decline, wane, dodder; senesce.