Does this mean clergy members today should have limitations placed on their material possessions?
ESV - 1 The Levitical priests, all the tribe of Levi, shall have no portion or inheritance with Israel. They shall eat the Lord 's food offerings as their inheritance.
For follow-up discussion and general commentary on the topic. Comments are sorted chronologically.
All Christians are priests under Jesus, the High priest. This is why scripture calls us a royal priesthood. There is no distinction between laity and clergy in this way.
Christians do not have an inheritance in current physical Israel, but rather in the kingdom of God.
Christians are also the temple of God which His presence in dwells by the spirit. So we 'serve the temple' by being a living sacrifice to God.