This is more than likely linked to the Communication Template against the step within your Job Approval Process.
If you check your process, you need to ensure that a Communication Template has been allocated to the step which emails aren't being received for.
If the Communication Template field is blank, this is why an email wouldn't be received;
You can allocate a template and save the process to rectify the issue.
If all the Communication Template fields have been populated, check to see that the relevant Team Member has been allocated when creating the vacancy - if may be the email has gone to another user;
There is usually a short delay on Job Approval emails being received, but depending on the usage of TalentLink at the time of using your new Approval Process, there can be a short delay on emails being received, therefore, if all of the above has been checked, please ensure you have waited 30-minutes for the email to come through.
Also, please ensure you have checked any Junk Mail folders where the email may have appeared.
If you are experiencing high volumes of Junk Mail, this could be a local IT setting - we have a Technical Requirements document available to give advice on the behaviour of emails within TalentLink, but please, check with your local IT department.