The recent discovery of a fast radio burst (FRB) in a globular cluster of M81 points to more than one channels for the formation of objects that produce these powerful radio pulses. Association of an FRB to a globular cluster (or other old stellar systems) suggests that strongly magnetized neutron stars, which are the most likely objects responsible for these bursts, are born not only when young massive stars undergo core-collapse, but also by mergers of old white dwarfs. We find that the fractional contribution to the total FRB rate by old stellar populations is at least a few percent, and the precise fraction can be constrained by FRB searches in the directions of nearby galaxies, both star-forming and elliptical ones. Using very general arguments, we show that the activity time of the M81-FRB is between 10^4 and 10^6 years under conservative assumptions, and more likely of order 10^5 years. The energetics of radio outbursts puts a lower limit on the magnetic field strength of 10^{13} G, and the spin period > 0.2 sec, thereby ruling out the source being a milli-second pulsar. The upper limit on the persistent X-ray luminosity (provided by Chandra), together with the high FRB luminosity and frequent repetitions, severely constrains (or rules out) the possibility that the M81-FRB is a scaled-up version of giant pulses from Galactic pulsars. Finally, the 50 ns variability time of the FRB lightcurve suggests that the emission is produced in a compact region inside the neutron star magnetosphere, as it cannot be accounted for when the emission is at distances > 10^{10} cm.
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