Councils across West Yorkshire and in York are trying to create a single set of rules for cabbies, in a bid to ensure regulation is the same all over the region.
In August it was revealed that a total of 21 drivers in Wakefield have lost their licence because of a criminal conviction since 2014.
Nearly two thirds of those were for driving offences.
Although cabbies do not lose their licence automatically if they offend, they must inform the local authority if they've been prosecuted. The council then judges each case on its merits.
Now drivers may be forced to wait longer to get their right to trade back if their crime is driving-related, though a length of time has not been specified.
In papers to be discussed by Wakefield Council's licensing committee next week, a report on the issue says: "The main difference between the current convictions policy and that proposed is a stricter approach to motoring convictions, with longer periods required before applicants/licence holders can be considered 'fit and proper'.
"Proposals on driver training see the introduction of refresher training and a test for safeguarding awareness."
If the proposals are backed by councillors, an eight-week consultation process with drivers and the travelling public will start.
The papers suggest that the cost of obtaining a licence, which has been a long-standing grievance for cabbies in Wakefield, may change depending on whether or not more or fewer applications are made.
The report adds: "Changes to policy may have an impact on the number of individuals who wish to and are eligible to hold a Wakefield taxi driver licence.
"Any significant changes to the number of licence holders could potentially influence the future cost of service/ income from fees.
"This position will continue to be monitored annually and reported as appropriate."
Concerns were raised earlier this year that drivers from Wakefield and elsewhere were travelling to Wolverhampton to obtain their licence, because their rules were felt to be less strict.
A 2015 law change means that cabbies can work and live anywhere in the UK with one licence from any local authority.
BBC figures show that Wolverhampton Council issued more than twice the number of private hire licences of any other local authority between March 2015 and March 2017.
In July, one driver was refused a licence renewal by Wakefield Council, though the public were barred from attending the meeting.
The local authority has subsequently refused to specify why the application was rejected.