(Imgur album for convenience: https://i.stack.imgur.com/IqNfp.jpg)
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These are five crossword-like structures: the first two clues are for the outer and inner ring (the latter of which can read starting from any point and in any direction), and the remaining five clues are for the five sides of the pentagram.
The completed grids are here:
The red-dotted letters spell STARFISH.
Each of the right-hand phrases clues a different phrase - for instance, a "secretive buzzer" is a CAGEY BEE. This sounds like you're spelling out KGB, which fits the "espionage" clue.
The list of solutions is:
In the image, some blanks for letters are circles instead of squares; the indicated letters spell GLASSWARE.
The clue answers are:
Each of these can be parsed as a boolean expression - so "PANDA" is "P AND A". In some cases, the given order of operations disambiguates.
As hinted by the 26 rectangles, we need to figure out which of the letters is true and false. The clues highlighted yellow (green in my screenshot) are to be taken as true, and the rest are false.
From FORD, GORU, JORD, LORD, VORW, WORX, QORE, HORRORCORE, [LANDF]ORM, KNORR, we rule out CDEFGHJKLMQRUVWX.
From ANANDA, A is true. From IXORA and PANDA, I and P are false.
From SANDS, S is false. From SNORT, T is true.
From BORG, B is true. From BANDZ, Z is false.
From NORMANDY, N is true. From NANDY, Y is false. From NOTHANDO, O is true.
Anagramming the true letters spells BATON, the "conductors' need" hinted in the flavortext.
Each of these clues is missing a certain number of letters from the front of all of its words:
___ On (Spurred) (5)
"HOw DO YOu LIke ___ APples?" (4)
OCCupying AN OTToman, PERhaps (6)
PREPared FOR A DECAthlon, FOR EXAMple (7)
YOU PLACE IT UNDERNeath A CHAMPAgne WINEGLass TO COUNTEract DISCOLouration OF A TABLECloth, E. G. (7)
The answers to these clues are EGGED, THEM, SEATED, TRAINED, ORDINARY, and COASTER. Each of these can also have the appropriate number of letters added to the front to make a new word, forming Legged, ANthem, NAUseated, CONStrained, EXTRAordinary, ROLLERcoaster.
The first letters of these spell LANCER.
The given cards are the 4 of Cups, the 5 of Swords, the 4 of Swords, the 4 of Wands, the 4 of Pentacles, the 5 of Wands, the 5 of Swords (again), and the 6 of Swords.
Indexing into the corresponding answers spells SE CORNER.
In the bottom-right corner of the Rider-Waite-Smith deck (where these pictures are taken from), artist Pamela Coleman Smith drew a small 'signature'. But the signatures here have been edited - instead of merging together her initials, they each display a letter and a number.
We can repeat the same process to get the final answer - tarot readers hear spirits with an EAR CANAL (which, as indicated by the pushed-up cards, has ARCANA right in the middle!)
Thanks to M Oehm and Stiv for helping me finish off this answer.