While making application for VAT did they request the EORI at the same time?
If not then trader should wait until they receive the VAT and then apply for EORI.
If trader applies now for EORI while VAT application is in progress they will receive the EORI but it will cause issues as it will not be linked to VAT and it will be generic one.
More information on EORI is on below link where they can contact EORI team by filling online contact form.
Get an EORI number