Hello Erika,
which module do you have?If you check the release notes of your future version (it is supported):
https://support.f5.com/kb/en-us/products/big-ip_ltm/releasenotes/product/relnote-bigip-ve-13-1-0.html
https://support.f5.com/kb/en-us/products/big-ip_ltm/releasenotes/related/relnote-supplement-bigip-13-1-0-4.html
Regarding the the potential problematic, All depends on your configuration and the modules you have (ASM, APM, LTM).
you just need to schedule a maintenance period and correct any problems. I made this type of upgrades several times and I already had some problems but nothing complicated:
-> ASM policy corruption ( check a service that has ASM to validate that this module work fine if not look at the logs). I already had to redo entire policies. To validate that you have a problem in your ASM Policy, remove IT from your VS and test it...
-> LTM: if the configuration load in general it goes well thereafter. possibly some profile to modify but it is rare
...
I think the best is to manage this aspect during the upgrade and correct any problematic (the possible edge effects that you will have depend on your configuration)...
but if you have time and you want a little more comfort you can do it in 2 steps through 11.6.2
then 13...
Regards