The Age Cryptic by DH #20,801

I got beaten by this one. I couldn't solve19D or 13D. I barely got 9D and still can't parse it. Yet there were quite a few wee gems in there that I was able to share with the Cryptic Crossword Learners group on Facebook.

I was frustrated by three clues that used the word "in" in a way that I've not been accustomed, so help me clarify if this was acceptable use of those "in"s or am I right and they're being used in a misleading and unfair manner.

6D - In New York look over new synthetic fibre (5)

It's a beginning and endings type clue that usually gets a signpost to hint to looking at the start or end of a word but here DP uses "in" which is usually a hidden word or container signpost. I had just shrugged and moved on thinking it was probably fine and I was being a pedant, but then...

14A - Sister in business beat puzzling question (9)

"Sister" = NUN and "business" = CO but "nun" isn't going "in" anything, it's going after the CO. Leaving "beat" = DRUM for CO(NUN)(DRUM) which again left me thinking "in" was used in an unfair way. "After" would've been better, "followed" or similar. That would make it kosher, right?

17D - Blimey! Half full in Ionian Island (5)

Now I'm being over-observant, I appreciate that. Here the "in" is probably meant to be a misdirection to a hidden word. Using the word "on" instead would be an issue for making the clue easier and removing the misdirection. I can see the difference but doesn't mean I still don't like it's use.

Here's my pic:

19D - Loses the block when rents go up high (4,3)

I think for 19D I'm a bit stuck on the TV show The Block which I never watch but I see "rents" = LETS and "goes up high" = FLY but I don't know what the rest is all about.

13D - Hearten companion? Always poetic? (5)

I didn't understand why "companion" = CH but I know "always poetic" = E'ER. A short companion for "CHum" or something? I don't know.

9A - Looked up if Tegan in trouble removing drug from her drink (14)

I think "IF TEGAN" is partial anagram fodder but I've not figured out the rest of the clue. It's probably very simple or I'm missing  something obvious but by the time dinner rolled around I was mentally done and wanted to go play Fallout 4 and shoot stuff.

I have started DP and off to a promising start. I'll post that later if I finish it off. Happy Hump Day.