Hello ShahinMortazave,
Thank you for your question and reaching out.
I can understand you are facing AD replication.
Please note that as you have Added manually connection in NTDS settings then It should be automatically Replication from your HQ DC due KCC service which is responsible to adjust the connections. Also , Please verify Cost value for site link should be according to your speed of network.
KCC :
The KCC is a built-in process that runs on all domain controllers and generates replication topology for the Active Directory forest. The KCC creates separate replication topologies depending on whether replication is occurring within a site (intrasite) or between sites (intersite). The KCC also dynamically adjusts the topology to accommodate the addition of new domain controllers, the removal of existing domain controllers, the movement of domain controllers to and from sites, changing costs and schedules, and domain controllers that are temporarily unavailable or in an error state.
https://learn.microsoft.com/en-us/previous-versions/windows/it-pro/windows-server-2003/cc755326(v=ws.10)
I will also suggest to verify AD replication health using Active Directory Replication Status Tool
https://www.microsoft.com/en-in/download/details.aspx?id=30005
https://learn.microsoft.com/en-us/previous-versions/windows/it-pro/windows-server-2003/cc755326(v=ws.10)
--------------------------------------------------------------------------------------------------------------------------------
--If the reply is helpful, please Upvote and Accept as answer--