  We have obtained Keck spectra for 16 globular clusters (GCs) associated with
the merger remnant elliptical NGC 1052, as well as a long-slit spectrum of the
galaxy. We derive ages, metallicities and abundance ratios from simple stellar
population models using the methods of Proctor & Sansom (2002), applied to
extragalactic GCs for the first time. We find all of the GCs to be ~13 Gyr old
according to simple stellar populations, with a large range of metallicities.
  From the galaxy spectrum we find NGC 1052 to have a luminosity-weighted
central age of ~2 Gyr and metallicity of [Fe/H]~+0.6. No strong gradients in
either age or metallicity were found to the maximum radius measured (~1 kpc).
However, we do find a strong radial gradient in alpha-element abundance, which
reaches a very high central value. The young central starburst age is
consistent with the age inferred from the HI tidal tails and infalling gas of
\~1 Gyr. Thus, although NGC 1052 shows substantial evidence for a recent merger
and an associated starburst, it appears that the merger did not induce the
formation of new GCs, perhaps suggesting that little recent star formation
occurred. This interpretation is consistent with ``frosting'' models for
early-type galaxy formation. (Abridged)
