So,if there is no liaison with être, then the "s" in "je suis" is never "carried-over"?
For loss of a better example, if I were to say "je suis intelligent(e)", the "s" would not be attached to the "i" in "intelligent(e)" - right?
In French, the verb "être" (to be) is an exception when it comes to liaisons. Normally, liaisons occur when a word that ends with a consonant is followed by a word that begins with a vowel or a silent "h." However, with "être," liaisons are not made.
So, in your example, "je suis intelligent(e)," no liaison is made, and the "s" in "suis" is not carried over to "intelligent(e)." The pronunciation will be "je swee in-teh-lee-zhahn(t)" with a pause between "suis" and "intelligent(e)."
It's important to note that there are other cases where a liaison may occur with "être" but only in certain specific situations. For example, when using the present participle form of "être" with an adjective, such as "étant," a liaison may be made before a vowel sound following "étant." But in the specific case you mentioned, "je suis intelligent(e)," no liaison is made.