"Long-standing" sounds even worse to me, and googling/quacking finds only one instance, on reddit, while it finds a few more for just "long". I've heard "Her career has been long and successful", and "His career is long and diverse". Not commonly, but it doesn't sound completely wrong to me in the present tense (though that's not the tense in which it sounds best).
Except that "ça carrière" does not mean anything. "Ça" is short for "cela", a demonstrative pronoun meaning this, that, or it. It would be like saying "It career". "Ça" is not a possessive adjective (aka, determinant) such as son, sa, ton, ta, mon, ma, etc. "Sa" and "ça" sound alike but by understanding what the different words mean, you will never hear "sa carrière" as "ça carrière".
I sort of understand what you're saying, but isn't 'ça' also 'that'? If not, how would you say "(specifically) That career"? Example: "He wants to be a firefighter" "That career is dangerous" Since he is not a firefighter yet, you wouldn't say "Son carrièr" nor "Le carrièr" because your talking about a specific career.
In French, there are many words that are translated to English in multiple ways. The demonstrative adjectives "this" and "that" are represented by a single word. The form it takes depends on the gender of the noun it refers to. La carrière is a feminine noun so "that career" (or "this career") would be "cette carrière". Masculine gender nouns would use "ce" for this/that, (ce livre = this/that book). If the (masculine) noun begins with a vowel or vowel sound, you would use "cet", e.g., "cet ami" = this/that friend. The plural form is "ces", representing "these" or "those"; it does not change with the gender of the noun. http://french.about.com/od/grammar/a/adjectives_demonstrative.htm
There are also indefinite pronouns ceci (this), cela (that) or ça which can mean either this or that (pronoun, not adjective). http://french.about.com/od/grammar/a/adjectives-and-pronouns.htm