It seems that the key thing to consider is the issue of countability.
When a noun is countable and singular, in most cases it should take an article: either a or the. The problem with English is that a noun can be countable in one sense and uncountable in some other sense. Here's a dictionary entry for 'support' that lists its countable and uncountable senses.
The majority of the listed senses for support are uncountable, and only two are countable:
[countable] a thing that holds something and prevents it from falling.
[countable] something you wear to hold an injured or weak part of your body firmly in position
These countable senses clearly do not fit your purpose, and it's only a countable singular support that can take a:
John installed a support in the coal mine to make it safer.
John wears a knee support to help him walk.
The two examples of support above are countable; your support is uncountable, because its meaning leans towards "function", not some palpable, material thing. This sentence would sound strange:
This year, I've added Apple supports to ten different applications. (a bit strange)
You would say instead:
This year, I've added Apple support to ten different applications.
Compare with a countable-sense support:
This year, I've installed wooden supports in ten different coal mines.
When a noun is uncountable, it either takes the or takes no article. In order to take the, it should be definite. It's hard for me to expand your sentence to make it "definite enough", but I'll try:
We also added the basic Apple support that the customer requested last month. (the noun support is definite because we used the "that-clause" to make it definite)
But this sentence seems somewhat strange to me. It's more usual to use support in this context as a indefinite non-count noun:
We also added basic Apple support, as requested by the customer last month.
Examples of usage from Google Books:
HTML 4.01 1999 This version added support for style sheets to give Web designers greater control over page layout. (source)
A variant of 95b, called OSR 2.1, added rudimentary USB support. (source)
Besides expanded support and improved performance of NDS, now called NDS eDirectory, Novell added pure IP support. (source)
Furthermore, Google Ngram finds no instances of "added a support for", but does find instances of "added support for".
(a caveat: I'm not a native speaker of English, and articles are cryptic to me sometimes)