Hi @eunsol seo
You can start the Search Admin Web Service Instance is on a server with an Admin Component using the following PowerShell:
PowerShell Resolution:
$(Get-SPFarm).Servers["<ServerName>"].ServiceInstances |
Where {$_.TypeName -eq "Search Administration Web Service"} |
Start-SPServiceInstance
For more information about managing search components, you could refer to:
https://learn.microsoft.com/en-au/SharePoint/search/manage-search-components?redirectedfrom=MSDN
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