I can only give an imprecise answer to this question. When there are too few candidates to fill all seats, then those validly nominated are appointed. Provided they are a quorum they can act as a council. They can coopt additional members up to the council's full strength.
So far as I understand it, there is no option to call for a poll in this situation, nor any need to give public notice of the vacancies.
Whether there is time pressure, given a quorum, is hard to ascertain. My colleagues tend to agree with my view that it is distasteful to coopt immediately after an election, because anyone who wished to be a councillor should have put themselves forward to face the electorate. We have, therefore, in the past postponed any cooption so far as possible, and have not been put under undue pressure by the district council's chief legal officer, who was aware of our delay.
Last time this occurred we postponed cooption until a casual vacancy arose, at which point it was obligatory to give public notice of the option to call for a poll and to proceed with either the poll (if sufficient candidates are nominated) or with cooption for all the vacancies.
Some councils do coopt immediately after an election, and that is not unlawful.
CLARIFICATION: The power to co-opt exists for 35 days after an election that does not fill all council seats, but does fill enough to have a quorum. If the power to co-opt is not exercised, then the district council could step in and appoint councillors to make up the number. However, the district council is likely to have more pressing concerns, and may not exercise their power provided they think the council is being operated sensibly.
