Thats not the way how HTTP Basic Authentication works. You need a authentication mechanism with is capable of doing a kind of single sign on.
For now search guard can be setup do do this via kerberos (or NTLM in a windows infrastructure). The will soon be more support like oauth2 and SAML or CAS. Maybe for you also the unauthenticated feature is interesting, see:
# Authenticates always a user with username 'searchguard_unauthenticated_user'
#searchguard.authentication.http_authenticator.impl: com.floragunn.searchguard.authentication.http.HTTPUnauthenticatedAuthenticator
in combination with host based security (hosts attribute in acl)
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