can i pay for a single case tech support from Atlassian engineers?

[InfiniGlobe LLC]

We are having hard times upgrading our Jira Core/Software/Service Desk from 7.13.1 to any later LTS.

We are on Starter license. 

Is it possible to pay Atlassian team to help us on the matter?

[Daniel Ebers]

Hi @InfiniGlobe LLC

Starter licenses are not entitled for support requests.

You mention "hard times". In case you want to go into detail probably somebody from Community here is also able to help.
Many people with very good knowledge are here and except access to your system would be needed I would give it a try if I were you.

If this is not acceptable for you probably an Atlassian partner nearby is willing to help?
You can find a list of official partners here: https://partnerdirectory.atlassian.com/

Regards,
Daniel

[Jack Brickey]

you might consider contacting a local Atlassian Partner too. They are often very experienced w/ upgrades.

[Deepanshu Natani]

If you can elaborate on what exact issues you are facing while upgrading, we (community members) might be able to provide you some inputs.

Also as suggested by @Daniel Ebers and @Jack Brickey you can reach out to Atlassian Solution Partners to assist you if you do not wish to elaborate here.