  We propose a universal framework to compute record age statistics of a
stochastic time-series that undergoes random restarts. The proposed framework
makes minimal assumptions on the underlying process and is furthermore suited
to treat generic restart protocols going beyond the Markovian setting. After
benchmarking the framework for classical random walks on the $1$D lattice, we
derive a universal criterion underpinning the impact of restart on the age of
the $n$th record for generic time-series with nearest-neighbor transitions.
Crucially, the criterion contains a penalty of order $n$, that puts strong
constraints on restart expediting the creation of records, as compared to the
simple first-passage completion. The applicability of our approach is further
demonstrated on an aggregation-shattering process where we compute the typical
growth rates of aggregate sizes. This unified framework paves the way to
explore record statistics of time-series under restart in a wide range of
complex systems.
