  We study constraints on Composite Higgs models with fermion partial
compositeness from electroweak precision measurements, including the 2022
$W$-boson mass result from the CDF collaboration. We focus on models where the
Composite Higgs sector arises from underlying four-dimensional strongly
interacting gauge theories with fermions, and where the SM fermions obtain
their mass via linear mixing terms between the fermions and the composite
sector -- the so-called fermion partial compositeness scenario. In general, the
Composite Higgs sector leads to a small and positive $S$ parameter, and a
negative $T$ parameter, but the fermion partial compositeness sector results in
an overall positive $T$ parameter in a large part of parameter space. We,
therefore, find good agreement between the full composite models and the
current electroweak precision measurement bounds on $S$ and $T$ from LEP and
CDF, including the offset and correlation of $S,T$ with respect to the SM
predictions.
