The gap seems to get close by retainer but it all depends on the possibility of level of attachment of frenum. Basically a frenum is a fibre of muscle underneath upperlip which gets attached on the gums just above the teeth in the centre. So this fibre poses a problem that even if the gap is closed by the retainer or any other orthodontic aid the gap will reapper due to the fibre. So first see that off, when you are having a consultation with dentist.
Next Steps
change of crown can also solve the problem but better have last word of the treating dentist.
Health Tips
you have crooked lower teeth as well go for a full braces treatment for complete improvement of bite.