In general a Deputy Mayor (or Vice-Chairman) has all the function of The Mayor (or Chairman) when acting in that capacity. However, if an allowance was specifically allocated to The Mayor, it would not automatically be available to the deputy when acting in the official capacity. If though, the council were to resolve that expenses might be claimed say pro rata depending on the number and type of engagements for example, then clearly there would be a facility for the Deputy Mayor to claim expenses. The answer to this lies in any agreed policy of the council mindful of the principle that any councillor may claim for out of pocket expenses.