Suggesting my words are false introduces pressure (8)
I believe the answer is:
implying
'suggesting' is the definition.
(implying is a kind of suggesting)
'are false introduces pressure' is the wordplay.
'are' becomes 'im' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'false' becomes 'lying' (I've seen this in another clue).
'introduces' indicates putting letters inside.
'pressure' becomes 'p' (abbreviation).
'im'+'lying'='imlying'
'imlying' placed around 'p' is 'IMPLYING'.
'my words' acts as a link.
I am not very happy about this link. Some or all of it may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for implying that I've seen before include "making insinuations" , "Insinuating; signifying" , "Suggesting" , "Meaning" , "Indicating by suggestion" .)