Low temperature ac magnetic susceptibility measurements of the coexistent antiferromagnetic superconductor YbPd2Sn have been made in hydrostatic pressures < 74 kbar in moissanite anvil cells. The superconducting transition temperature is forced to T(SC) = 0 K at a pressure of 58 kbar. The initial suppression of the superconducting transition temperature is corroborated by lower hydrostatic pressure (p < 16 kbar) four point resisitivity measurements, made in a piston cylinder pressure cell. At ambient pressure, in a modest magnetic field of ~ 500 G, this compound displays reentrant superconducting behaviour. This reentrant superconductivity is suppressed to lower temperature and lower magnetic field as pressure is increased. The antiferromagnetic ordering temperature, which was measured at T(N) = 0.12 K at ambient pressure is enhanced, to reach T(N) = 0.58 K at p = 74 kbar. The reasons for the coexistence of superconductivity and antiferromagnetism is discussed in the light of these and previous findings. Also considered is why superconductivity on the border of long range magnetic order is so much rarer in Yb compounds than in Ce compounds. The presence of a new transition visible by ac magnetic susceptibility under pressure and in magnetic fields greater than 1.5 kG is suggested.