  The longitudinal or transverse spin transfer to Lambda and anti-Lambda
hyperons in polarized proton-proton collisions is expected to be sensitive to
the helicity or transversity distributions of strange and anti-strange quarks
of the proton, and to the corresponding polarized fragmentation function. We
report the first measurement of the transverse spin transfer to $\Lambda$ and
$\bar \Lambda$ along the polarization direction of the fragmenting quark,
$D_{TT}$, in transversely polarized proton-proton collisions at 200 GeV with
the STAR experiment at RHIC. The data correspond to an integrated luminosity of
18 pb$^{-1}$, and cover a kinematic range of |$\eta$|< 1.2 and transverse
momentum $p_T$ up to 8 GeV/c. We also report an improved measurement of the
longitudinal spin transfer $D_{LL}$ to $\Lambda$ and $\bar \Lambda$ with $p_T$
up to 6 GeV/c, using data with about twelve times larger figure-of-merit than
the previously published STAR results. The prospects of hyperon polarization
measurements in the forward pseudo-rapidity region (2.5<$\eta$<4) in p+p
collision in the year of 2021 and beyond will also be discussed, which is based
on the STAR forward detector upgrade plan including a forward tracking system
and a forward calorimeter system.
