Victoria
DLA and PI is not effected by UC.
Unless there is a specific requirement for you to claim UC, which there will not be unless you make a new claim for something like Housing Benefit, then you will stay on your current ESA claim.
At some time in the future, possibly from 2020 onwards, ESA claimants will be transferred to UC and New ESA, but at this time there are no details of how the transfer will be achieved..
Gordon
Nothing on this board constitutes legal advice - always consult a professional about specific problems