Richard Tennison or Tenison (1642 – 29 July 1705) was an Irish bishop of Killala, Clogher and Meath.
He was born the eldest son of Thomas Tennison of Carrickfergus and matriculated from Trinity College, Dublin in 1659.
He was made headmaster of the Diocesan School at Trim. In 1671 he was presented as Rector and Vicar of Laracor and in 1675 he was appointed Rector of Louth and Dean of Clogher. On 19 February 1682 he was consecrated Bishop of Killala and Achonry, a position he held until he was translated to Clogher on 28 February 1691. From there he was translated a second time on 25 June 1697 to Meath, where he remained until his death in 1705.