  We have investigated energies, magnetic dipole hyperfine structure constants
($A_{hyf}$) and electric dipole (E1) matrix elements of a number of low-lying
states of the triply ionized tin (Sn$^{3+}$) by employing relativistic
coupled-cluster theory. Contributions from the Breit interaction and
lower-order quantum electrodynamics (QED) effects in determination of above
quantities are also given explicitly. These higher-order relativistic effects
are found to be important for accurate evaluation of energies, while QED
contributions are seen to be contributing significantly to the determination of
$A_{hyf}$ values. Our theoretical results for energies are in agreement with
one of the measurements but show significant differences for some states with
another measurement. Reported $A_{hyf}$ will be useful in guiding measurements
of hyperfine levels in the stable isotopes of Sn$^{3+}$. The calculated E1
matrix elements are further used to estimate oscillator strengths, transition
probabilities and dipole polarizabilities ($\alpha$) of many states. Large
discrepancies between present results and previous calculations of oscillator
strengths and transition probabilities are observed for a number of states. The
estimated $\alpha$ values will be useful for carrying out high precision
measurements using Sn$^{3+}$ ion in future experiments.
