The agreement was put in place in 1952 after the parish agreed to sell a plot of land in Bellozanne Valley to the States at a reduced price to enable the construction of the former incinerator.
In return, St Helier was allowed to dispose of its rubbish and waste water for free.
In September 2016, the department took the parish to court to abolish the agreement as it wanted to introduce an Island-wide commercial waste charge.
It was felt the new charge could not be introduced if one parish was to be exempt.
The Infrastructure Department won the case, and a subsequent appeal by the parish was rejected by the Court of Appeal.
In a parish assembly next Wednesday, town residents will be asked whether they want Constable Simon Crowcoft to lodge a proposition with the States to call for the covenant to be maintained.
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