ComplexHeatmap::draw has a padding paramater: padding of the plot. Elements correspond to bottom, left, top, right paddings.

library(ComplexHeatmap)
set.seed(1)
m <- matrix(sample(c(0,1), replace=T, size=20*8), nrow=20) |> 
  `colnames<-`(rep("pneumonoultramicroscopicsilicovolcanoconiosis", 8)) |> 
  make_comb_mat()
ComplexHeatmap::draw(UpSet(t(m)), padding = unit(c(30, 2, 2, 2), "mm"))

_{Note: For the next time, please provide a How to make a great r reproducible example}