  Recently born magnetars are promising candidates for the engines powering
fast radio bursts (FRBs). The focus thus far has been placed on millisecond
magnetars born in rare core-collapse explosions, motivated by the star forming
dwarf host galaxy of the repeating FRB 121102, which is remarkably similar to
the hosts of superluminous supernovae (SLSNe) and long gamma-ray bursts (LGRB).
However, long-lived magnetars may also be created in binary neutron star (BNS)
mergers, in the small subset of cases with a sufficiently low total mass for
the remnant to avoid collapse to a black hole, or in the accretion-induced
collapse (AIC) of a white dwarf. A BNS FRB channel will be characterized by
distinct host galaxy and spatial offset distributions than the SLSNe/LGRB
channel; we anticipate a similar host population, although possibly different
offset distribution for AIC events. We show that both the BNS and AIC channels
are consistent with the recently reported FRB 180924, localized by ASKAP to a
massive quiescent host galaxy with an offset of about 1.4 effective radii.
Using models calibrated to FRB 121102, we make predictions for the dispersion
measure, rotation measure, and persistent radio emission from magnetar FRB
sources born in BNS mergers or AIC, and show these are consistent with upper
limits from FRB 180924 for reasonable parameters. Depending on the rate of AIC,
and the fraction of BNS mergers leaving long-lived stable magnetars, the birth
rate of repeating FRB sources associated with older stellar populations could
be comparable to that of the core-collapse channel. We also discuss potential
differences in the repetition properties of these channels, as a result of
differences in the characteristic masses and magnetic fields of the magnetars.
